We analyze Weierstrass cycles and tautological rings in moduli space of smooth algebraic curves and in moduli spaces of integral algebraic curves with embedded disks with special attention to moduli spaces of curves having genus $leq 6$. In particula
r, we show that our general formula gives a good estimate for the dimension of Weierstrass cycles for lower genera.
We study the multiplication and comultiplication in equivariant cohomology of Sato Grassmannian
We calculate the homomorphism of the cohomology induced by the Krichever map of moduli spaces of curves into infinite-dimensional Grassmannian. This calculation can be used to compute the homology classes of cycles on moduli spaces of curves that are defined in terms of Weierstrass points.
